A305395 Records in A073053 starting from a(1).

11, 101, 112, 202, 213, 303, 314, 404, 415, 505, 516, 606, 617, 707, 718, 808, 819, 909, 9110, 10010, 10111, 11011, 11112, 21012, 31013, 41014, 51015, 61016, 71017, 81018, 91019, 101020, 111021, 121022, 131023, 141024, 151025, 161026, 171027, 181028, 191029

Offset

1,1

Comments

The record-holders are the powers of 2 written in base 4, A004643.

Not all record terms of A073053 have index in A004643. For instance, a(22) = 11011 = A073053(10111111111). - Chai Wah Wu, Nov 19 2025

All record-holders are of one of the forms 2*10^k or 10^k+(10^j-1)/9 with 0 <= j <= k. - Pontus von Brömssen, Jan 14 2026

Links

Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Matthew E. Coppenbarger, Iterations of a modified Sisyphus function, Fib. Q., 56 (No. 2, 2018), 130-141.

Prog

(Python)
from itertools import count, islice
def A305395_gen(): # generator of terms
    c = 0
    for n in count(1):
        l = len(s:=str(n))
        m = int(str(e:=sum(1 for d in s if d in {'0', '2', '4', '6', '8'}))+str(l-e)+str(l))
        if m>c:
            yield m
            c = m
A305395_list = list(islice(A305395_gen(), 15)) # Chai Wah Wu, Nov 19 2025
(Python)
from itertools import count
def candidate_values():
    for k in count(1): # number of digits in record-holder candidates
        s = str(k)
        for i in range(1, k+1): # number of odd digits
            yield int(str(k-i)+str(i)+s)
        yield int(s+'0'+s) # no odd digit
def A305395_gen():
    M = 0
    for x in candidate_values():
        if x > M:
            yield x
            M = x # Pontus von Brömssen, Jan 14 2026

Crossrefs

Cf. A073053, A004643.

Sequence in context: A247647 A240602 A117697 * A158051 A091366 A073064

Adjacent sequences: A305392 A305393 A305394 * A305396 A305397 A305398

Keyword

nonn,base

Author

N. J. A. Sloane, Jun 25 2018

Extensions

a(11)-a(22) from Chai Wah Wu, Nov 19 2025

a(23)-a(25) from Chai Wah Wu, Jan 13 2026

a(26)-a(41) from Pontus von Brömssen, Jan 14 2026

Status

approved